PROCEEDINGS OF THE 31st ICRC, ŁÓDŹ 20091

Study on angular resolution of GRAPES-3 array
A.Oshima∗ , S.R.Dugad∗, T.Fujii† , U.D.Goswami∗ , S.K.Gupta∗ , Y.Hayashi†, N.Ito† ,P.Jagadeesan∗, A.Jain∗ , S.Karthikeyan∗, S.Kawakami†, H.Kojima‡ , T.Matsuyama†,
M.Minamino† , H.Miyauchi†, P.K.Mohanty∗, S.D.Morris∗, P.K.Nayak∗, T.Nonaka†,
S.Ogio† , T.Okuda†, B.S.Rao∗, K.C.Ravindran∗, M.Sasano†, K.Sivaprasad†,
H.Tanaka†, S.C.Tonwar∗, E.Usui† , Y.Yamashita†∗ Tata Institute of Fundamental Research† Osaka City University, Japan‡ Aichi Institute of Technology

Keywords: cosmic ray, angular resolution, Moonshadow
I. I NTRODUCTION
Since the γ-ray flux from a source has to be detected,against a huge background contributed by the isotropic
flux of the cosmic rays, it is necessary to achieve as
good a rejection of this background as possible forthe detection system. For a point source, the signal tobackground ratio is inversely proportional to the squareof the angular resolution. Therefore, the most important
requirement of an EAS detector system is its angularresolution for maximizing the signal to background ratio.
The technique of relative arrival timing has been used
extensively in the EAS arrays, for the determination ofthe arrival direction of the showers [1], [2], [3].
II. E XPERIMENTAL S YSTEM
The experimental system of the GRAPES-3 (Gamma
Ray Astronomy at PeV EnergyS Phase-3) experimentconsists of a densely packed array of scintillator detectors and a large area tracking muon detector. The EAS
array consists of 257 plastic scintillator detectors, each8060

a40b20[m]Abstract. GRAPES-3 experiment at Ooty in India,
constitutes of about 300 scintillator detectors, is aconventional air shower array which detects air
showers produced by primary high energy cosmic
rays. The detectors are placed in a equilateral triangle shape with distance of 8m. Good anglar resolution
is required for search of gamma ray point sourcesthat is one of the main goal of GRAPES-3. Hence,
the relative arrival time of particle in an air shower
plane arriving at each detectors is an importantparameter which is effectively used for thei reconstruction of arrival direction of primary particles.
Here, we will discuss on the angular resolution of
the present GRAPES-3 experiment by using the two
important methods such as EvenOdd and RightLeftmethods. The new results obtained from the above
two methods have been compared with the outcomeof the Moon and the Sun shadow observation, andwill be presented elaborately.

0−20−40−60−80−80−60−40−20 0[m]204060Fig. 1. The GRAPES-3 experimental system with 257 scintillator
detectors and 16 muon detector modulesof 1 m2 in area. These detectors are deployed with aninter-detector separation of only 8 m. The array is being
operated at Ooty in south India (11.4◦N, 76.7◦ E, 2200 m
altitude).
In order to achieve the lowest possible energy threshold, a simple 3-line coincidence of detectors has beenused to generate the Level-0 trigger, which acts as thefast GATE and START for the analog to digital and time
to digital converters (ADCs and TDCs), respectively.
As expected, this trigger selects a large number ofvery small and local showers and also larger showers
whose cores land very far from the physical area of thearray. Therefore, it is also required that at least 10 outof the inner 127 detectors should have triggered theirdiscriminators within 1 µs of the Level-0 trigger. This
Level-1 trigger with an observed EAS rate of 13 Hz isused to record the charge (ADC) and the arrival time(TDC) of the pulses from each detector [4]. The pulse
charge is later converted into the equivalent numberof minimum-ionizing particles (MIPS) using the mostprobable charge for a single MIP measured using thetrigger from a small area (20×20 cm2 ) scintillation
counter telescope.

2A.OSHIMA et al. GRAPES-3 ANGULAR RESOLUTION

III. GRAPES-3 A NGULAR R ESOLUTION
A total of 1.4×109 showers have been collected overa total live-time of 9.4×107s, spread over a four year
period, from 2000 to 2003. For each EAS, the core
location, the shower age ‘s’ representing the steepnessof the Nishimura-Kamata-Greisen (NKG) lateral distribution function and the shower size Ne have been
determined [5]. This was done by using the observed
particle densities, following the minimization procedure
discussed in detail elsewhere [6]. Also, for each shower,
the zenith (θ) and the azimuthal (φ) angles have been
calculated using the time information from the TDCs,
following the minimization procedure described in [6].
As mentioned in the §I, one of the most criticalparameter in the search for the point sources of cosmic
γ-rays, using a particle detector array is its angularresolution. An improvement in the angular resolution
allows the rejection of a larger fraction of the background EAS, initiated by the charged cosmic rays. Thisin turn would increase the signal to background ratio
and may enable the discovery of the new cosmic γray sources. This requires an accurate determination of
the relative arrival time of the shower front at various
detectors and an accurate determination of the shapeof the shower front. Since the detectors in the EAS
array are distributed over a large area and exposed tothe outside weather, the timing accuracy is affected by
the temperature dependence of the response of various
components of the scintillation detector system. Observations have shown that the temperature coefficient forthe scintillator, the photomultiplier, the signal cables, andthe electronic modules (amplifiers, discriminators andthe TDCs) are significantly different from each otherand undergo measurable variations.
IV. T HE EVEN - ODD METHODThe EAS detectors in the GRAPES-3 array are sequentially numbered from the centre outwards, withthe detector number increasing clockwise over eachsuccessive hexagonal ring. Therefore, it was decided
to divide the array in two sub-arrays, namely, the firstwith the even-numbered and the second with the oddnumbered detectors. Next, a comparison of the arrival
directions determined independently with the two subarrays, labeled ‘even’ and ‘odd’, respectively, is carriedout. Since these two sub-arrays have a very substantial
spatial overlap, they provide similar estimate of theEAS direction and also an important insight into the
angular determination capability of the experiment [7].
An important limitation of this approach arises from thesystematic errors that are common to both of the subarrays and therefore can not be measured. But, due tothe spatial overlap of the ‘even’ and ‘odd’ sub-arrays,
the direction determined by them would contain thesame systematic error. In this method, event cut wasimposed on the core location of the shower to lie within
the hexagon labeled ‘a’, as shown in Fig. 1. Since thedata from these two sub-arrays are independent of eacho

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150200Fig. 2. Variation of the median angle as a function of the number ofdetectors triggered.

other, the actual error in the determination of the angle
is smaller by a factor of √12 , than the value quotedabove. Since, only half of the total number of detectors
triggered, are used in each of the two sub-arrays, theangular resolution for the full array would be smaller
by a further factor of √12 .
In Fig. 2, the median angle, which is an alternative
measure of the angular resolution of our array, is shown
as a function of the number of detectors triggered.
The magnitude of the median angle initially decreases
rapidly with increasing number of triggered detectors up
to ∼50 detectors, indicating rapid improvement in theangular resolution. However, thereafter the improvement
is relatively slower.
V. T HE LEFT- RIGHT METHOD
Here, we present the results of a study that demonstrates the existence of the curvature in the shower
front. A considerable improvement is seen in the angularresolution when a cone-shape is used to describe thecurvature in the shower front. The curvature of theshower front is easily studied by dividing the array into
two independent halves, namely, the left and the righthalf-arrays. For this purpose the following procedure
is adopted. First, the location of the shower core isdetermined and then the line joining the shower corewith the centre of the array is used to divide thearray into the left- and the right-half arrays. Although
this array division is implemented on an event-to-event
basis, yet this procedure ensures that the number ofdetectors triggered in each of the two half-arrays areapproximately equal.
In the even-odd case, the density of the detectors isreduced by a factor of 2, while the area of the each subarray remains nearly the same as the area ‘A’ of thefull array. However, in the left-right case the density ofthe detectors remains unchanged, but the area of eachhalf-array gets reduced by a factor of 2 to A
2 . Therefore,
we expect the ratio of the areas in the two cases to be
2. Since the angular resolution is inversely proportional
to the linear extent of the array, we expect the angular

PROCEEDINGS OF THE 31st ICRC, ŁÓDŹ 2009
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50100150200Fig. 3. Variation of the median angle, (a) αmp for plane fit shownby filled circles , (b) αmc for cone fit shown by filled squares, as afunction of number of detectors triggered.

resolution to worsen by a factor of √12 in the leftright case, as compared to the even-odd case. Thus acorrection by a factor of √12 is required when comparing
the results from the above methods.
In Fig. 3, the median angle αmp is shown as filledcircles, as a function of the number of hit detectors.
The magnitude of αmp shows a very small change withincreasing number of triggered detectors, right up to 200detectors.

Fig. 4. (a) A 2-D map of % variation in number of showers fromthe directions around the Moon. The map is centred on the Moon andcovers ±5◦ in R.A. and declination. A significant decrease is seen ina region of ∼1.5◦ around the Moon.

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VI. S HADOWS OF M OON AND S UN
It is well-known that the observations of the shadowof the Moon or the Sun cast on the flux of cosmic rays
observed at the Earth provides an ideal method to determine the angular resolution of an EAS array. It allows
both, the statistical error in the angle determination as
well as the systematic error in pointing towards a given
direction to be measured.
The following procedure has been adopted for theanalysis of the GRAPES-3 data. (a) Divide the fieldof view around the centre of the Moon or the Sun, inconcentric circles of equal solid angle area Next, thenumber of showers incident along directions lying ineach concentric bin are counted. The inner most bin(disk) has a diameter of 0.5◦ , which equals the angular
diameter of the Moon. The solid angle of each bin
is 6×10−5sr, which therefore equals the solid angle
projected by the Moon or the Sun. (b) For determining
the background, similar concentric circles are drawn
centred at two different directions, on either side of theMoon (or the Sun) that are offset by 8◦ in the azimuthal
angle, but at the same zenith angle. This selection of thebackground region ensures that the shower attenuation inboth the Moon/Sun and background regions is identical,
allowing a direct comparison of the shower rates in thetwo regions to be made.
Fig. 4, the 2-dimensional map of the number ofshowers arriving from the directions around the Moon
are shown. The map is centred on the Moon and covers

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Fig. 5. (a) A 2-D map of % variation in number of showers aroundthe Sun. The map is centred on Sun and covers ±5◦ in R.A. anddeclination. A significant decrease seen in a region of ∼2◦ ×2◦ aroundthe Sun.

±5◦ both in the right ascension and the declination. The
shadow of the Moon on the primary cosmic ray flux
is clearly visible in Fig. 4. We had employed a 2-D
Gaussian to describe the study the angular resolution ofour array. Similarly in §VI, to measure the effect of theshadows of the Moon and the Sun, we again employeda 2-D Gaussian fit.
Now, we display the shadow of the Sun in a 2dimensional map of the number of showers arriving fromthe directions around the Sun in Fig. 5. This map iscentred on the Sun and covers ±5◦ both in the rightascension and declination. Once again the effect of theshadow of the Sun is visible in Fig. 5, although it appears
to be much more fuzzy than the shadow of the Moon
as shown in Fig. 4. We observed the shadowing effects
from the direction of the Sun, although with significantly
larger fluctuations. This is not unexpected, since ourobservations during 2000-2003 coincided with the periodof maximum solar activity.

4A.OSHIMA et al. GRAPES-3 ANGULAR RESOLUTION

is consistent with a null value. The Sun data also yields
a similar value of the angular resolution, although withsignificantly larger uncertainty for the reasons mentionedin §VI. We conclude that the high density of the detectors
in the GRAPES-3 experiment has been instrumental in
obtaining the observed angular resolution.

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R EFERENCESo0.4020406080100TeVFig. 6. Variation of angular resolution with primary energy (TeV) bymethods, (a) left-right, filled triangles , (b) even-odd, filled squares ,(c) Moon shadow, filled circles

VII. D ISCUSSION
For a direct comparison of the angular resolutionof the GRAPES-3 array by the use of three different
methods, we have converted the shower size Ne into
the energy of the primary protons, using the CORSIKA
Monte Carlo simulation program, version 6.500 with
the QGSJet generator [8]. A comparison of the angularresolution of the GRAPES-3 array, as determined by thethree completely different methods namely; the evenodd, the left-right and the Moon shadow, as outlined in§IV, §V, §VI respectively, are shown in Fig. 6. For theeven-odd case the angular resolution is extracted fromthe 2-D Gaussian fit to the angular distribution of events
for a given number of detectors triggered. This value isdivided by 2 as explained in §IV to obtain the true valueof the angular resolution.
VIII. S UMMARY
We have analyzed the EAS data collected by theGRAPES-3 experiment over the four year period from2000 to 2003. The division of the array into even andodd sub-arrays is used to estimate the shower energy dependent angular resolution of the GRAPES-3 array. An
alternative method of estimating the angular resolution
by using the concept of left and right half-arrays withcone-shaped shower front has yielded a value of 0.5◦ ,which is slightly larger than the value of 0.4◦ obtainedby the even-odd method for showers of energy ≥80 TeV.
The even-odd method provides the best estimate of
the angular resolution attainable in an array free fromsystematic errors. The agreement between the angularresolution obtained from the even-odd and the left-rightmethods provides the evidence, that the cone-shaped
shower front used in determining the shower direction isan adequate representation of the shower disk. Finally,
the reduction in the isotropic flux of the cosmic rays dueto the shadow of the Moon yields an angular resolutionof 0.5◦ for showers of energy ≥80 TeV. The absolute
pointing accuracy of the GRAPES-3 arrays is ∼0.2◦ andthe small offset observed, based on the present data set,

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